WRITTEN EXERCISES.

198. 1. Reduce .4, .36, and .035 to similar fractions.

ANALYSIS.-Since the lowest order of decimals is thousandths, all the decimals must be changed to thousandths.

Since annexing ciphers to a decimal does not alter its value (Prin.), we give to each number three decimal places by annexing

ciphers, thus making them similar.

RULE. Give to all the decimals the same number of places

199. To reduce a decimal to a common fraction.

1. If 5 tenths is written as a common fraction, what is the numerator? What is the denominator?

2. What is the numerator and what the denominator of 12 hundredths when expressed as a common fraction?

3. Express the value of the decimal 20 hundredths by a common fraction in its smallest terms.

WRITTEN EXERCISES.

200. 1. Reduce .75 to its equivalent common fraction.

ANALYSIS.-.75 expressed as a common frac

tion is, which, being reduced to its smallest terms, is 2.

RULE.Omit the decimal point, supply the denominator, and reduce the fraction to its smallest terms.

Reduce the following to common fractions in their small

201. To reduce a common fraction to a decimal.

1. How many tenths are there in ? In 2. How many hundredths are there in ? 3. How many hundredths are there in 1? 4. How many thousandths are there in 1? 5. How many tenths are there in ? In

?

In

?

In

? In ?

In

? In ?

? In ? In ?

WRITTEN EXERCISES.

1. Reduce to an equivalent decimal.

PROCESS. 8)5.000

625

ANALYSIS.- is of 5, or of 50 tenths; and of 50 tenths is 6 tenths and 2 tenths remaining. 2 tenths are equal to 20 hundreths, and of 20 hundredths is 2 hundredths and 4, hundredths remaining. 4 hundredths are equal to 40 thousandths, and of 40 thousandths is 5 thousandths. Hence is equal to 6 tenths+2 hundredths +5 thousandths, or .625.

RULE.-Annex ciphers to the numerator and divide by the denominator. Point off as many decimal places in the quotient as there are ciphers annexed.

In many cases the division is not exact. In such instances the remainder may be expressed as a common fraction, or the sign+ may be employed after the decimal to show that the result is not complete; thus: .1663, or .166 +.

=

PRINCIPLES.-The principles are the same as for addition of

common fractions.

203. 1. What is the sum of 1.36, 3.253, and .0453?

PROCESS.

=

ANALYSIS. The numbers are written

1.36 = 1.3600 so that units stands under units, tenths under tenths, etc.

=3.2530

3.253

.0453

=

0453

4.6583 4.6583

The decimals may be made similar by annexing ciphers and then added, care being taken to place the decimal point in

the sum directly under the decimal point in the numbers added. Or, Since only units of one order are found in any column, it is unnecessary, in practice, to make them similar.

Find the sum of the following:

16. What is the sum of 9 hundredths, 45 thousandths, 8 tenths, and 146 thousandths?

17. What is the sum of 354 thousandths, 213 millionths, 3564 hundred-thousandths, 9 tenths, and 18 hundredths?

18. A merchant's sales were as follows: On Monday $369.34, on Tuesday $296.18, on Wednesday $473.39, on Thursday $468.37. How much were they for those four days?

19. A pedestrian walked 49.13 miles the first day, 33.13 the second day, 46.19 the third day, and 39.47 miles on the fourth day. How far did he travel in the four days?

SUBTRACTION OF DECIMALS.

204. 1. From take. From .8 take .3. 2. From take. From .12 take .07. 3. From 4 take. From 3 take .3.

4. From 6 take 2,5%. From 7 take 4.3.

PRINCIPLES.- The principles are the same as for subtraction of common fractions.

WRITTEN EXERCISES.

205. 1. From 24.23 subtract 8.5624.

PROCESS.

24.23

8.5624

24.2300 8.5624 15.6676 15.6676

ANALYSIS.--The numbers are written so that units stand under units, tenths under tenths, etc.

The decimals may be made similar and then subtracted, care being taken to place the decimal point in

the remainder directly under the decimal point in the numbers subtracted.

In the first process the ciphers are written, but they may be supposed to be annexed when we subtract, and consequently need not be written.

10. What is the difference between 6.285 and 3.2846? 11. What is the difference between 4.83 and .4836? 12. What is the difference between 3.28 and .0436? 13. From 65 hundredths subtract 65 hundred-thousandths. 14. From 193 ten-thousandths subtract 1426 millionths. 15. From 97 thousandths subtract 456 ten-thousandths. 16. Find the value of 2.35 - .064 +3.23 17. Find the value of 3.572 + 2.36 .425. -2.6142. 18. Find the value of 5.23 +.329

-1.2356.

- 4.164.00045.

19. Find the value of 4.6+2.3506 - 1.004-3.3.

20. Find the value of 3.8004-1.00006 +3.7 4.0405. 21. The receipts of a manufactory were $18269.25 and the expenses were $11243.59. What was the gain?

22. A railroad ticket agent sold in 1880 tickets to the value of $13269.43, and in 1881 to the value of $17839.54. How much did the sales in 1881 exceed the sales in 1880?

MULTIPLICATION OF DECIMALS.

206. 1. What is the product of × 2? .4 × 2? 2. How many decimal figures are there in the product of tenths by units?

3. What is the product of X 4? .04 X 2?

4. How many decimal figures are there in the product of hundredths by units?

of?

5. What is the product of X? .4.2?